Problem: A circle with area $81\pi$ has a sector with a $\dfrac{6}{5}\pi$ radian central angle. What is the area of the sector? {81\pi} \color{#9D38BD}{\dfrac{6}{5}\pi} {\dfrac{243}{5}\pi}
Solution: The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{6}{5}\pi \div 2 \pi = \dfrac{A_s}{81\pi}$ $\dfrac{3}{5} = \dfrac{A_s}{81\pi}$ $\dfrac{3}{5} \times 81\pi = A_s$ $\dfrac{243}{5}\pi = A_s$